Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include <iostream>
#include <iomanip>
#include <vector>
#include <algorithm>
using namespace std;

int main() {
  int n;
  cin >> n;
  vector<long long> a(n);
  int i;
  for (i = 0; i < n; i++) {
    cin >> a[i];
  }
  sort(a.begin(), a.end());
  long long min_diff = a[1] - a[0];
  for (i = 1; i < n - 2; i++) {
    min_diff = min(min_diff, a[i] - a[i - 1]);
  }
  long double result = ((long double)(a[n - 1] + a[n - 2])) / ((long double)(min_diff));
  result = max(result, ((long double)(a[n - 3] + a[n - 4])) / ((long double)(a[n - 1] - a[n - 2])));
  cout << setprecision(12) << result << endl;
  return 0;
}